coding-test

Read in Data

Read in the csv file, explore the data and create summary information.

# read in the csv file
ut_data <- read.csv("~/Downloads/urine_test_data.csv")

#examine structure
dim(ut_data)

## [1] 1000   33

names(ut_data)

##  [1] "Sample_ID"     "Organism_1"    "Organism_2"    "Organism_3"   
##  [5] "Organism_4"    "Organism_5"    "Organism_6"    "Organism_7"   
##  [9] "Organism_8"    "Organism_9"    "Organism_10"   "Antibiotic_1" 
## [13] "Antibiotic_2"  "Antibiotic_3"  "Antibiotic_4"  "Antibiotic_5" 
## [17] "Antibiotic_6"  "Antibiotic_7"  "Antibiotic_8"  "Antibiotic_9" 
## [21] "Antibiotic_10" "Antibiotic_11" "Antibiotic_12" "Antibiotic_13"
## [25] "Antibiotic_14" "Antibiotic_15" "Antibiotic_16" "Antibiotic_17"
## [29] "Gene_1"        "Gene_2"        "Gene_3"        "Gene_4"       
## [33] "Gene_5"

str(ut_data)

## 'data.frame':    1000 obs. of  33 variables:
##  $ Sample_ID    : chr  "Sample_0001" "Sample_0002" "Sample_0003" "Sample_0004" ...
##  $ Organism_1   : int  675 692 0 811 708 0 0 0 738 234 ...
##  $ Organism_2   : int  291 377 173 0 553 0 64 0 0 278 ...
##  $ Organism_3   : int  0 0 0 710 0 0 0 0 0 73 ...
##  $ Organism_4   : int  204 0 0 0 0 678 687 0 0 0 ...
##  $ Organism_5   : int  666 0 0 0 0 0 0 0 0 0 ...
##  $ Organism_6   : int  0 971 25 0 0 0 0 0 0 0 ...
##  $ Organism_7   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Organism_8   : int  0 0 0 485 0 0 0 0 0 0 ...
##  $ Organism_9   : int  799 0 0 0 0 0 0 0 0 0 ...
##  $ Organism_10  : int  0 0 0 0 0 0 659 0 0 0 ...
##  $ Antibiotic_1 : chr  "R" "R" "R" "R" ...
##  $ Antibiotic_2 : chr  "R" "R" "R" "R" ...
##  $ Antibiotic_3 : chr  "R" "R" "R" "R" ...
##  $ Antibiotic_4 : chr  "S" "S" "R" "S" ...
##  $ Antibiotic_5 : chr  "R" "R" "S" "R" ...
##  $ Antibiotic_6 : chr  "R" "R" "R" "R" ...
##  $ Antibiotic_7 : chr  "S" "R" "S" "S" ...
##  $ Antibiotic_8 : chr  "R" "R" "R" "S" ...
##  $ Antibiotic_9 : chr  "R" "R" "R" "R" ...
##  $ Antibiotic_10: chr  "R" "R" "R" "R" ...
##  $ Antibiotic_11: chr  "R" "R" "R" "R" ...
##  $ Antibiotic_12: chr  "R" "R" "S" "S" ...
##  $ Antibiotic_13: chr  "S" "R" "S" "S" ...
##  $ Antibiotic_14: chr  "S" "R" "R" "S" ...
##  $ Antibiotic_15: chr  "R" "S" "S" "R" ...
##  $ Antibiotic_16: chr  "S" "S" "S" "S" ...
##  $ Antibiotic_17: chr  "S" "S" "S" "R" ...
##  $ Gene_1       : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ Gene_2       : int  0 1 0 0 0 1 1 0 0 0 ...
##  $ Gene_3       : int  0 0 0 0 0 1 1 0 0 0 ...
##  $ Gene_4       : int  0 0 0 0 0 0 0 0 0 1 ...
##  $ Gene_5       : int  0 0 0 0 0 0 0 0 0 0 ...

summary(ut_data)

##   Sample_ID           Organism_1      Organism_2      Organism_3   
##  Length:1000        Min.   :  0.0   Min.   :  0.0   Min.   :  0.0  
##  Class :character   1st Qu.:  0.0   1st Qu.:  0.0   1st Qu.:  0.0  
##  Mode  :character   Median :  0.0   Median :  0.0   Median :  0.0  
##                     Mean   :190.5   Mean   :182.7   Mean   :120.9  
##                     3rd Qu.:350.2   3rd Qu.:358.0   3rd Qu.:  0.0  
##                     Max.   :999.0   Max.   :997.0   Max.   :999.0  
##    Organism_4       Organism_5       Organism_6       Organism_7    
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00  
##  Median :  0.00   Median :  0.00   Median :  0.00   Median :  0.00  
##  Mean   : 98.72   Mean   : 91.23   Mean   : 69.51   Mean   : 58.12  
##  3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.00  
##  Max.   :994.00   Max.   :988.00   Max.   :998.00   Max.   :994.00  
##    Organism_8       Organism_9      Organism_10     Antibiotic_1      
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Length:1000       
##  1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   Class :character  
##  Median :  0.00   Median :  0.00   Median :  0.00   Mode  :character  
##  Mean   : 43.16   Mean   : 37.65   Mean   : 33.11                     
##  3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.00                     
##  Max.   :992.00   Max.   :998.00   Max.   :997.00                     
##  Antibiotic_2       Antibiotic_3       Antibiotic_4       Antibiotic_5      
##  Length:1000        Length:1000        Length:1000        Length:1000       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  Antibiotic_6       Antibiotic_7       Antibiotic_8       Antibiotic_9      
##  Length:1000        Length:1000        Length:1000        Length:1000       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  Antibiotic_10      Antibiotic_11      Antibiotic_12      Antibiotic_13     
##  Length:1000        Length:1000        Length:1000        Length:1000       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##  Antibiotic_14      Antibiotic_15      Antibiotic_16      Antibiotic_17     
##  Length:1000        Length:1000        Length:1000        Length:1000       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##      Gene_1          Gene_2         Gene_3          Gene_4          Gene_5     
##  Min.   :0.000   Min.   :0.00   Min.   :0.000   Min.   :0.000   Min.   :0.000  
##  1st Qu.:0.000   1st Qu.:0.00   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000  
##  Median :0.000   Median :0.00   Median :0.000   Median :0.000   Median :0.000  
##  Mean   :0.317   Mean   :0.24   Mean   :0.172   Mean   :0.097   Mean   :0.038  
##  3rd Qu.:1.000   3rd Qu.:0.00   3rd Qu.:0.000   3rd Qu.:0.000   3rd Qu.:0.000  
##  Max.   :1.000   Max.   :1.00   Max.   :1.000   Max.   :1.000   Max.   :1.000

# Create lists of each group of variables
org_col <- c("Organism_1","Organism_2","Organism_3","Organism_4","Organism_5","Organism_6",
             "Organism_7","Organism_8","Organism_9","Organism_10")

antibio_col <- c("Antibiotic_1","Antibiotic_2","Antibiotic_3","Antibiotic_4","Antibiotic_5","Antibiotic_6",
                 "Antibiotic_7","Antibiotic_8","Antibiotic_9","Antibiotic_10","Antibiotic_11","Antibiotic_12",
                 "Antibiotic_13","Antibiotic_14","Antibiotic_15","Antibiotic_16","Antibiotic_17")

gene_col <- c("Gene_1","Gene_2","Gene_3","Gene_4","Gene_5")

# make sure Sample_ID is a factor varaible
ut_data$Sample_ID <- factor(ut_data$Sample_ID)

# Add new summary data to the wide dataframe
ut_data$numorg_count <- rowSums(ut_data[org_col]>0)
ut_data$uti_present <- (ut_data$numorg_count>0) 
ut_data$numAR_count <- (rowSums(ut_data[antibio_col]=="R")) 
ut_data$AR_present <- (ut_data$numAR_count>0) 
ut_data$numgene_count <- (rowSums(ut_data[gene_col])) 
ut_data$gene_present <- (ut_data$numgene_count>0) 


# create long dataframes for graphics
ut_data_org_long <- gather(ut_data[c("Sample_ID",org_col)], 
                      Organism, count, Organism_1:Organism_10, factor_key = TRUE)
ut_data_anti_long <- gather(ut_data[c("Sample_ID",antibio_col)], 
                       Antibiotic, status, Antibiotic_1:Antibiotic_17, factor_key = TRUE)
ut_data_gene_long <- gather(ut_data[c("Sample_ID",gene_col)], 
                       Gene, status, Gene_1:Gene_5, factor_key = TRUE)


# Create dataframe for organism PCA, set rownames at Sample_ID
ut_data_org_pca <- ut_data[org_col] 
rownames(ut_data_org_pca) <- ut_data[,1]

Data Visualization and Analysis

This is fairly straightforward. Each graphic drives home that this is simulated data. There is a beutiful stepped percentage of antibiotic resistance. Same goes for the Genes. I assume “Genes” are bacterial genes and not germline human genes in the subject noting that individual’s PGx metabolism. The Gene’s by subject grph is really crowded, so I seperated it into 10 of ~100 subjects each. The Organism cell count distribution is again ver similar, with just a slight variation in subjects/count for each organism.

# Percent Antibiotic Resistance
ggplot(ut_data_anti_long, aes(x=Antibiotic, y = prop.table(stat(count)), fill=factor(status)), 
                                label = scales::percent(prop.table(stat(count)))) +
      geom_bar(colour = "black", position = "fill") + scale_y_continuous(labels = scales::percent) +
      scale_fill_brewer(palette = "Pastel1") + scale_x_discrete(guide = guide_axis(n.dodge = 2)) +
      geom_text(aes(label=signif(..count.. / tapply(..count.., ..x.., sum)[as.character(..x..)], digits=3)),
           stat="count", position=position_fill(vjust=0.5)) +
      labs(y="Proportion", fill = "AR Status") + ggtitle("Percentage of samples with Antibiotic resistance for each Antibiotic") +
      theme(plot.title = element_text(color="black",size = 24, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

#Table format
table(ut_data_anti_long$Antibiotic, ut_data_anti_long$status=="R")

##                
##                 FALSE TRUE
##   Antibiotic_1     98  902
##   Antibiotic_2    158  842
##   Antibiotic_3    168  832
##   Antibiotic_4    213  787
##   Antibiotic_5    280  720
##   Antibiotic_6    321  679
##   Antibiotic_7    366  634
##   Antibiotic_8    408  592
##   Antibiotic_9    444  556
##   Antibiotic_10   512  488
##   Antibiotic_11   546  454
##   Antibiotic_12   565  435
##   Antibiotic_13   604  396
##   Antibiotic_14   667  333
##   Antibiotic_15   707  293
##   Antibiotic_16   759  241
##   Antibiotic_17   777  223

# Presence of each gene across samples
ggplot(ut_data_gene_long[], aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) + 
  labs(y="Sample ID", fill = "Gene Presence") + ggtitle("Presence or Absence of Genes 1 through 5 for each sample ") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 24, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

#Table format
table(ut_data_gene_long$Gene, ut_data_gene_long$status=="1")

##         
##          FALSE TRUE
##   Gene_1   683  317
##   Gene_2   760  240
##   Gene_3   828  172
##   Gene_4   903   97
##   Gene_5   962   38

# You cannot read the Sample_IDs on the graph with 1000 rows. Instead lets generate 10 graphs with ~100 rows each.
ggplot(subset(ut_data_gene_long, grepl("^Sample_00",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) + 
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 1:99 ") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_01",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 100:199 ") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_02",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 200:299") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_03",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 300:399") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_04",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 400:499") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_05",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 500:599") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_06",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 600:699") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_07",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 700:799") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_08",Sample_ID)), aes(x=Gene, y=Sample_ID )) + geom_tile(aes(fill = factor(status))) +
  labs(y="Sample ID", fill = "Gene Presence") +ggtitle("Presence or Absence of Genes 1 through 5 for each sample 800:899") +
  scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

ggplot(subset(ut_data_gene_long, grepl("^Sample_09",Sample_ID) | grepl("^Sample_1",Sample_ID)), aes(x=Gene, y=Sample_ID )) + 
  geom_tile(aes(fill = factor(status))) + labs(y="Sample ID", fill = "Gene Presence") + 
  ggtitle("Presence or Absence of Genes 1 through 5 for each sample 900:1000") + scale_fill_manual(values = c("darkblue","lightblue")) +
  theme(plot.title = element_text(color="black",size = 22, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

# distributions of each organism across all samples

ggplot(ut_data_org_long, aes(x=count, color=Organism)) + geom_density() +
  ggtitle("Distribution of cell counts for each organism") + scale_fill_brewer(palette = "Pastel1") +
  theme(plot.title = element_text(color="black",size = 24, face = "bold"),axis.title = element_text(color="black",size = 12, face = "bold"))

#Table format
table(ut_data_org_long$Organism, ut_data_org_long$count>0)

##              
##               FALSE TRUE
##   Organism_1    620  380
##   Organism_2    646  354
##   Organism_3    766  234
##   Organism_4    794  206
##   Organism_5    829  171
##   Organism_6    848  152
##   Organism_7    880  120
##   Organism_8    903   97
##   Organism_9    929   71
##   Organism_10   937   63

Additional Analysis

If this data were real I would look to see if the oraganism cell counts correlate with each other (they don’t see the ggpairs output). I would calculate the total number of samples with at least one active organism, but also look at the distribution for how many organism are in a common UTI. For this case I assume ANY cells cell count>0 is equivalent to infection. This may not be the case, but it is my baseline assumption for this analysis. 894 samples have at least 1 organism, while 106 samples have no organism on the test. The median and IQR for the number of organisms per sample is 2{1:3}.

I would do the same for Antibiotic resistance to the 17 antibiotics and the 5 genes. It turns out every sample is resistant to at least 4 Antibiotics with median{IQR} resitance to 9{8-11}. This seems odd or impossible since 106 samples have no UTI organisms, and therefore cannot possibly have antibiotic resistance. Again, I am not sure what the “Genes” are counting, but if these are bacterial genes, it may again be impossible for someone with no organism to have genes present. Bothe of these issues would lead me to question the validity of the assay.

# organism cross-correlation
ggpairs(ut_data[org_col])

# organism present 
table(ut_data$uti_present)

## 
## FALSE  TRUE 
##   106   894

ggplot(ut_data, aes(x=numorg_count, )) + geom_bar() 

summary(ut_data$numorg_count)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   1.000   2.000   1.848   3.000   6.000

# resitance to antibiotics
table(ut_data$AR_present)

## 
## TRUE 
## 1000

ggplot(ut_data, aes(x=numAR_count, )) + geom_bar() 

summary(ut_data$numAR_count)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.000   8.000   9.000   9.407  11.000  15.000

# gene present
table(ut_data$gene_present)

## 
## FALSE  TRUE 
##   366   634

ggplot(ut_data, aes(x=numgene_count, )) + geom_bar() 

summary(ut_data$numgene_count)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.000   1.000   0.864   1.000   3.000

# Gene vs Organisms present
addmargins(table(ut_data$gene_present, ut_data$uti_present))

##        
##         FALSE TRUE  Sum
##   FALSE    41  325  366
##   TRUE     65  569  634
##   Sum     106  894 1000

MCMC analysis

First 4 antibiotics vs all organism.

The instructions were very unclear as to what was being predicted. Due to this vagueness, I chose to model both directions, at least for some of the variables. I really don’t think the version predicting antibiotic resistance was working correctly, so I abandoned it after 4 antibiotics. No Organism cell count predicted the presence or absence of Antibiotic resistance for the first four antibiotics.

# While both of these sections could have been run in a loop, I specifically chose to write out each command 
# separately to see the exact command implemented for each model.


ut_data$AB1 <- 0
ut_data$AB1[ut_data$Antibiotic_1=="R"] <- 1

ut_data$AB2 <- 0
ut_data$AB2[ut_data$Antibiotic_2=="R"] <- 1

ut_data$AB3 <- 0
ut_data$AB3[ut_data$Antibiotic_3=="R"] <- 1

ut_data$AB4 <- 0
ut_data$AB4[ut_data$Antibiotic_4=="R"] <- 1


AB1_stan <- stan_glm(AB1 ~ Organism_1 + Organism_2 + Organism_3 + Organism_4 + Organism_5 + 
                       Organism_6 + Organism_7 + Organism_8 + Organism_9 + Organism_10, 
                     family = binomial(link = "logit"),prior = NULL, data=ut_data)

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AB1_stan_m <- as.matrix(AB1_stan)

AB2_stan <- stan_glm(AB2 ~ Organism_1 + Organism_2 + Organism_3 + Organism_4 + Organism_5 + 
                       Organism_6 + Organism_7 + Organism_8 + Organism_9 + Organism_10, 
                     family = binomial(link = "logit"),prior = NULL, data=ut_data)

## 
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AB2_stan_m <- as.matrix(AB2_stan)

AB3_stan <- stan_glm(AB3 ~ Organism_1 + Organism_2 + Organism_3 + Organism_4 + Organism_5 + 
                       Organism_6 + Organism_7 + Organism_8 + Organism_9 + Organism_10, 
                     family = binomial(link = "logit"),prior = NULL, data=ut_data)

## 
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AB3_stan_m <- as.matrix(AB3_stan)

AB4_stan <- stan_glm(AB4 ~ Organism_1 + Organism_2 + Organism_3 + Organism_4 + Organism_5 + 
                       Organism_6 + Organism_7 + Organism_8 + Organism_9 + Organism_10, 
                     family = binomial(link = "logit"),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'bernoulli' NOW (CHAIN 1).
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AB4_stan_m <- as.matrix(AB4_stan)


# AB1
posterior_interval(AB1_stan, prob=0.95)

##                      2.5%        97.5%
## (Intercept)  1.8539379299 2.5440979150
## Organism_1  -0.0005084820 0.0009080416
## Organism_2  -0.0006473404 0.0008360838
## Organism_3  -0.0008101723 0.0007949352
## Organism_4  -0.0005248155 0.0014626546
## Organism_5  -0.0006831493 0.0012342639
## Organism_6  -0.0007176635 0.0016643302
## Organism_7  -0.0012617447 0.0009373192
## Organism_8  -0.0016127100 0.0007673674
## Organism_9  -0.0015643593 0.0008918133
## Organism_10 -0.0011991572 0.0018155503

plot(AB1_stan)

ppc_dens_overlay(y = AB1_stan$y, yrep = posterior_predict(AB1_stan, draws = 50))

mcmc_trace(AB1_stan_m )

# AB2
posterior_interval(AB2_stan, prob=0.95)

##                      2.5%        97.5%
## (Intercept)  1.3921275351 1.9911968192
## Organism_1  -0.0006718512 0.0004500575
## Organism_2  -0.0007126956 0.0004088690
## Organism_3  -0.0003087402 0.0011037011
## Organism_4  -0.0003155872 0.0013095802
## Organism_5  -0.0010070356 0.0003858738
## Organism_6  -0.0003056876 0.0017193868
## Organism_7  -0.0012830476 0.0003657222
## Organism_8  -0.0007265931 0.0016455885
## Organism_9  -0.0009246771 0.0014580556
## Organism_10 -0.0014598865 0.0008007833

plot(AB2_stan)

ppc_dens_overlay(y = AB2_stan$y, yrep = posterior_predict(AB2_stan, draws = 50))

mcmc_trace(AB2_stan_m )

# AB3
posterior_interval(AB3_stan, prob=0.95)

##                      2.5%        97.5%
## (Intercept)  1.2677149289 1.831979e+00
## Organism_1  -0.0005104311 5.978137e-04
## Organism_2  -0.0010820721 1.374872e-05
## Organism_3  -0.0004691592 8.931984e-04
## Organism_4  -0.0007251242 7.251541e-04
## Organism_5  -0.0002033521 1.405529e-03
## Organism_6  -0.0002273277 1.656712e-03
## Organism_7  -0.0004273550 1.541926e-03
## Organism_8  -0.0009005421 1.369282e-03
## Organism_9  -0.0003867583 2.223015e-03
## Organism_10 -0.0007015486 1.919641e-03

plot(AB3_stan)

ppc_dens_overlay(y = AB3_stan$y, yrep = posterior_predict(AB3_stan, draws = 50))

mcmc_trace(AB3_stan_m )

# AB4
posterior_interval(AB4_stan, prob=0.95)

##                      2.5%         97.5%
## (Intercept)  1.2790369177  1.814430e+00
## Organism_1  -0.0007560362  2.026844e-04
## Organism_2  -0.0008900241  9.891353e-05
## Organism_3  -0.0006856375  4.398353e-04
## Organism_4  -0.0006457228  6.820609e-04
## Organism_5  -0.0006531774  6.536820e-04
## Organism_6  -0.0014128630 -2.069166e-05
## Organism_7  -0.0004770176  1.332487e-03
## Organism_8  -0.0016261302  1.455036e-04
## Organism_9  -0.0013731107  4.479878e-04
## Organism_10 -0.0002911874  2.295085e-03

plot(AB4_stan)

ppc_dens_overlay(y = AB4_stan$y, yrep = posterior_predict(AB4_stan, draws = 50))

mcmc_trace(AB4_stan_m )

Organism as Outcome Variable vs 17 antibiotic resitance variables.

This may be the original intention of this exercise. At least this direction has some significant output. For example, Organism2 cell size appears to have a positive association with Antibiotic resistance to AB3 and AB16. Several other organism show slight associations with one or more antibiotics. See the posterior interval tables and interval plots for which may Antibiotics may be significant. Any 95% interval that does not include “0” may be significantly associated with that organism’s cell count.

# While both of these sections could have been run in a loop, I specifically chose to write out each command 
# separately to see the exact command implemented for each model.

# Build out models
org1_stan <- stan_glm(Organism_1 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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org1_stan_m <- as.matrix(org1_stan)

org2_stan <- stan_glm(Organism_2 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.6e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org2_stan_m <- as.matrix(org2_stan)

org3_stan <- stan_glm(Organism_3 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.9e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org3_stan_m <- as.matrix(org3_stan)

org4_stan <- stan_glm(Organism_4 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.7e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org4_stan_m <- as.matrix(org4_stan)

org5_stan <- stan_glm(Organism_5 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.6e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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## Chain 4: Gradient evaluation took 1.1e-05 seconds
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org5_stan_m <- as.matrix(org5_stan)

org6_stan <- stan_glm(Organism_6 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 2e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org6_stan_m <- as.matrix(org6_stan)

org7_stan <- stan_glm(Organism_7 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 2.2e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## Chain 2: Gradient evaluation took 1.2e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org7_stan_m <- as.matrix(org7_stan)

org8_stan <- stan_glm(Organism_8 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.9e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org8_stan_m <- as.matrix(org8_stan)

org9_stan <- stan_glm(Organism_9 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.9e-05 seconds
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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org9_stan_m <- as.matrix(org9_stan)

org10_stan <- stan_glm(Organism_10 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                        Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                        Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                     family = gaussian(),prior = NULL, data=ut_data)

## 
## SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
## Chain 1: 
## Chain 1: Gradient evaluation took 1.7e-05 seconds
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org10_stan_m <- as.matrix(org10_stan)

# model diagnostics
# org1
posterior_interval(org1_stan, prob=0.95)

##                      2.5%     97.5%
## (Intercept)    148.561030 316.82328
## Antibiotic_1S  -80.773704  50.59366
## Antibiotic_2S  -47.125269  55.88995
## Antibiotic_3S  -52.719355  45.82423
## Antibiotic_4S  -21.992968  73.40344
## Antibiotic_5S  -48.366729  37.84137
## Antibiotic_6S  -70.116416  10.07100
## Antibiotic_7S  -47.772259  30.85727
## Antibiotic_8S  -67.040447  12.12567
## Antibiotic_9S  -48.977096  28.86469
## Antibiotic_10S -27.953967  46.26708
## Antibiotic_11S -17.222817  61.62823
## Antibiotic_12S -34.652821  44.42883
## Antibiotic_13S  -5.376953  71.28476
## Antibiotic_14S -55.656754  27.37090
## Antibiotic_15S -58.952653  20.60584
## Antibiotic_16S -61.481357  25.96089
## Antibiotic_17S -68.906872  21.60202
## sigma          294.408777 321.84675

plot(org1_stan)

ppc_dens_overlay(y = org1_stan$y, yrep = posterior_predict(org1_stan, draws = 50))

mcmc_trace(org1_stan_m )

# org2
posterior_interval(org2_stan, prob=0.95)

##                      2.5%     97.5%
## (Intercept)     45.632984 203.66634
## Antibiotic_1S  -66.582505  53.91644
## Antibiotic_2S  -36.551453  62.75136
## Antibiotic_3S    9.291554 107.47275
## Antibiotic_4S  -16.712582  74.14336
## Antibiotic_5S  -30.862366  52.76299
## Antibiotic_6S  -47.668667  28.32247
## Antibiotic_7S  -13.838549  62.30070
## Antibiotic_8S   -9.999097  64.29174
## Antibiotic_9S  -25.943635  50.78890
## Antibiotic_10S -16.271467  55.78870
## Antibiotic_11S -24.797408  47.12190
## Antibiotic_12S -53.942924  23.04457
## Antibiotic_13S -32.265771  41.57003
## Antibiotic_14S -70.609540  10.22694
## Antibiotic_15S -67.230700  13.98810
## Antibiotic_16S   9.934913  96.07911
## Antibiotic_17S -40.190365  49.66852
## sigma          283.425535 309.89830

plot(org2_stan)

ppc_dens_overlay(y = org2_stan$y, yrep = posterior_predict(org2_stan, draws = 50))

mcmc_trace(org2_stan_m )

# org3
posterior_interval(org3_stan, prob=0.95)

##                      2.5%      97.5%
## (Intercept)    -24.792487 122.617380
## Antibiotic_1S  -48.374383  61.913713
## Antibiotic_2S  -61.924801  24.099692
## Antibiotic_3S  -55.855668  28.217835
## Antibiotic_4S  -32.534469  47.270015
## Antibiotic_5S  -10.504173  62.823014
## Antibiotic_6S  -17.417647  52.279349
## Antibiotic_7S  -61.440670   5.055894
## Antibiotic_8S  -21.963485  43.880799
## Antibiotic_9S  -16.075355  49.694738
## Antibiotic_10S -12.579160  52.519018
## Antibiotic_11S -13.106675  53.397456
## Antibiotic_12S -10.174790  55.810490
## Antibiotic_13S  -2.826854  63.505808
## Antibiotic_14S -17.136014  52.529003
## Antibiotic_15S -37.356858  35.146998
## Antibiotic_16S -29.141389  44.177109
## Antibiotic_17S -50.378788  28.901201
## sigma          250.732125 273.664602

plot(org3_stan)

ppc_dens_overlay(y = org3_stan$y, yrep = posterior_predict(org3_stan, draws = 50))

mcmc_trace(org3_stan_m )

# org4
posterior_interval(org4_stan, prob=0.95)

##                     2.5%      97.5%
## (Intercept)     37.50771 167.925604
## Antibiotic_1S  -70.42824  25.867928
## Antibiotic_2S  -63.07578  18.449287
## Antibiotic_3S  -35.54123  43.026462
## Antibiotic_4S  -26.97607  43.240501
## Antibiotic_5S  -45.20993  19.379569
## Antibiotic_6S  -45.61242  16.676562
## Antibiotic_7S  -42.48861  17.224468
## Antibiotic_8S  -15.97429  43.852300
## Antibiotic_9S  -10.29065  46.070218
## Antibiotic_10S -22.92659  35.675769
## Antibiotic_11S -46.20813  12.238117
## Antibiotic_12S -55.83398   2.823017
## Antibiotic_13S -60.87290  -2.240137
## Antibiotic_14S -24.94709  35.714574
## Antibiotic_15S -17.59120  48.507002
## Antibiotic_16S -28.55925  40.270616
## Antibiotic_17S  -7.68056  60.712081
## sigma          222.67655 243.184061

plot(org4_stan)

ppc_dens_overlay(y = org4_stan$y, yrep = posterior_predict(org4_stan, draws = 50))

mcmc_trace(org3_stan_m )

# org5
posterior_interval(org5_stan, prob=0.95)

##                      2.5%      97.5%
## (Intercept)     42.881346 172.552675
## Antibiotic_1S  -61.933061  35.237422
## Antibiotic_2S  -19.345562  58.629444
## Antibiotic_3S  -63.971585  11.028006
## Antibiotic_4S  -29.422738  41.105211
## Antibiotic_5S  -44.919179  22.572244
## Antibiotic_6S  -18.801922  44.491955
## Antibiotic_7S  -49.777320   9.544217
## Antibiotic_8S  -33.527487  25.023617
## Antibiotic_9S  -10.716713  47.397048
## Antibiotic_10S -29.802663  29.059225
## Antibiotic_11S -40.876747  16.285832
## Antibiotic_12S -42.648114  15.333082
## Antibiotic_13S -21.867940  36.248435
## Antibiotic_14S  -8.733794  54.949986
## Antibiotic_15S -31.222603  30.730773
## Antibiotic_16S -35.691241  33.241095
## Antibiotic_17S -60.560148  11.633385
## sigma          223.879910 244.552707

plot(org5_stan)

ppc_dens_overlay(y = org5_stan$y, yrep = posterior_predict(org5_stan, draws = 50))

mcmc_trace(org5_stan_m )

# org6
posterior_interval(org6_stan, prob=0.95)

##                      2.5%      97.5%
## (Intercept)     37.210025 146.666346
## Antibiotic_1S  -54.609004  26.636336
## Antibiotic_2S  -54.694546  14.640465
## Antibiotic_3S  -55.320849  11.167338
## Antibiotic_4S    4.921670  66.901235
## Antibiotic_5S  -53.937240   2.562963
## Antibiotic_6S  -30.812687  22.037263
## Antibiotic_7S  -36.426617  15.617986
## Antibiotic_8S  -36.950712  15.431381
## Antibiotic_9S  -42.024225   7.641835
## Antibiotic_10S -33.690604  16.507243
## Antibiotic_11S -27.859988  21.258911
## Antibiotic_12S -14.290543  35.104322
## Antibiotic_13S -34.228422  16.672481
## Antibiotic_14S  -9.757856  42.799020
## Antibiotic_15S -34.649056  19.815140
## Antibiotic_16S -41.083679  17.008380
## Antibiotic_17S -13.778317  45.580985
## sigma          191.205804 209.238510

plot(org6_stan)

ppc_dens_overlay(y = org6_stan$y, yrep = posterior_predict(org6_stan, draws = 50))

mcmc_trace(org6_stan_m )

# org7
posterior_interval(org7_stan, prob=0.95)

##                       2.5%      97.5%
## (Intercept)    -11.5702116  89.020982
## Antibiotic_1S  -30.8678603  46.596678
## Antibiotic_2S  -12.3383602  49.692878
## Antibiotic_3S  -42.8090063  17.331219
## Antibiotic_4S  -41.7323448  14.608259
## Antibiotic_5S   -8.1456094  41.322318
## Antibiotic_6S  -18.7879786  29.953864
## Antibiotic_7S  -21.9417804  24.430812
## Antibiotic_8S   12.1481628  59.569921
## Antibiotic_9S  -26.8669286  19.701259
## Antibiotic_10S -28.3509000  17.864265
## Antibiotic_11S -16.4360893  30.909100
## Antibiotic_12S -43.2904812   2.590936
## Antibiotic_13S -28.8328483  17.223930
## Antibiotic_14S -23.2038846  25.246259
## Antibiotic_15S -20.9705861  28.942315
## Antibiotic_16S   0.2753775  55.201414
## Antibiotic_17S -40.4527816  15.393842
## sigma          177.0263919 193.825527

plot(org7_stan)

ppc_dens_overlay(y = org7_stan$y, yrep = posterior_predict(org7_stan, draws = 50))

mcmc_trace(org7_stan_m )

# org8
posterior_interval(org8_stan, prob=0.95)

##                       2.5%     97.5%
## (Intercept)      0.8745323  90.33461
## Antibiotic_1S  -17.0828283  52.07886
## Antibiotic_2S  -34.0927836  20.42635
## Antibiotic_3S  -28.6690885  23.96184
## Antibiotic_4S   -2.8293807  45.81140
## Antibiotic_5S  -28.2676644  15.18263
## Antibiotic_6S  -25.0909020  17.53140
## Antibiotic_7S  -29.2209754  10.74233
## Antibiotic_8S  -19.1039339  20.30916
## Antibiotic_9S  -22.7659497  17.33438
## Antibiotic_10S -29.3884420  10.85260
## Antibiotic_11S -24.3960134  15.26541
## Antibiotic_12S  -9.9360647  29.13487
## Antibiotic_13S -22.1419914  20.05771
## Antibiotic_14S -28.9586875  13.20044
## Antibiotic_15S -13.3480327  31.29439
## Antibiotic_16S -19.9832191  27.55874
## Antibiotic_17S -24.7729437  23.38354
## sigma          151.4579820 165.11507

plot(org8_stan)

ppc_dens_overlay(y = org8_stan$y, yrep = posterior_predict(org8_stan, draws = 50))

mcmc_trace(org8_stan_m )

# org9
posterior_interval(org9_stan, prob=0.95)

##                      2.5%      97.5%
## (Intercept)      5.598690  92.507592
## Antibiotic_1S  -19.810706  45.326416
## Antibiotic_2S  -31.233184  22.687343
## Antibiotic_3S  -38.551346  12.282911
## Antibiotic_4S   -9.857663  36.277329
## Antibiotic_5S  -18.817993  26.280605
## Antibiotic_6S  -33.120437   9.764766
## Antibiotic_7S  -14.810295  25.591481
## Antibiotic_8S   -2.646243  37.317936
## Antibiotic_9S  -17.393277  20.773321
## Antibiotic_10S -21.716969  17.537265
## Antibiotic_11S -29.016573  10.973076
## Antibiotic_12S -24.236124  14.313160
## Antibiotic_13S -25.368655  13.276704
## Antibiotic_14S -14.837650  27.351963
## Antibiotic_15S -29.127212  13.361596
## Antibiotic_16S -24.795596  20.978165
## Antibiotic_17S -28.563199  16.740810
## sigma          149.337489 163.565888

plot(org9_stan)

ppc_dens_overlay(y = org9_stan$y, yrep = posterior_predict(org9_stan, draws = 50))

mcmc_trace(org5_stan_m )

# org10
posterior_interval(org10_stan, prob=0.95)

##                       2.5%      97.5%
## (Intercept)    -35.9013617  42.795322
## Antibiotic_1S  -29.1014796  29.494250
## Antibiotic_2S   -9.6387919  38.696756
## Antibiotic_3S  -28.7231806  19.153707
## Antibiotic_4S  -36.6594017   8.129336
## Antibiotic_5S  -17.5981422  21.458348
## Antibiotic_6S  -17.2700651  21.813087
## Antibiotic_7S  -27.9759260   8.402205
## Antibiotic_8S  -30.3259571   7.102179
## Antibiotic_9S  -19.0340040  16.708526
## Antibiotic_10S -15.6325176  20.109410
## Antibiotic_11S -23.2676708  12.313713
## Antibiotic_12S -12.1132161  23.249988
## Antibiotic_13S   3.4137411  40.293597
## Antibiotic_14S -10.0675832  27.365963
## Antibiotic_15S  -0.4125649  39.550908
## Antibiotic_16S -24.4483779  18.252756
## Antibiotic_17S -10.8168252  31.789947
## sigma          137.6069001 150.272634

plot(org10_stan)

ppc_dens_overlay(y = org10_stan$y, yrep = posterior_predict(org10_stan, draws = 50))

mcmc_trace(org10_stan_m )

PCA analysis

The PCA analysis shows that this is random simulated data with very little underlying structure. The first 10 principal components have equal weight across their eigenvalues with a range of 11.4 to 8.5 across all 10 components.

ut_org_results <- prcomp(ut_data_org_pca, scale = TRUE)

biplot(ut_org_results, scale = 0, xlabs = rep("x",1000))

var_explained <- ut_org_results$sdev^2/sum(ut_org_results$sdev^2)
var_explained

##  [1] 0.11384763 0.11195903 0.10779085 0.10443637 0.10205856 0.09728071
##  [7] 0.09425264 0.09278389 0.09021369 0.08537663

#create scree plot
qplot(c(1:10), var_explained) + 
  geom_line() + 
  xlab("Principal Component") + 
  ylab("Variance Explained") +
  ggtitle("Scree Plot") +
  ylim(0, 1)

Overall, this is a very mediocre coding test if the priority for this position is analyzing clinical trials data. It really doesn’t help that most tests are negative, and some of the data makes no physiologic sense. The MCMC Bayesian analysis is not something that most Biostatisticians would ever really use. Especially since you will get similar results (at least identifying the same resistant Antibiotics) using regular linear regression. In my experience, it can be very difficult to get results accepted if you use overly complicated or less common statistical methods.

#glm model
org2_glm <- glm(Organism_2 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + 
                  Antibiotic_7 + Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + Antibiotic_12 + 
                  Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + Antibiotic_16 + Antibiotic_17, 
                family = gaussian(), data=ut_data)

summary(org2_glm)

## 
## Call:
## glm(formula = Organism_2 ~ Antibiotic_1 + Antibiotic_2 + Antibiotic_3 + 
##     Antibiotic_4 + Antibiotic_5 + Antibiotic_6 + Antibiotic_7 + 
##     Antibiotic_8 + Antibiotic_9 + Antibiotic_10 + Antibiotic_11 + 
##     Antibiotic_12 + Antibiotic_13 + Antibiotic_14 + Antibiotic_15 + 
##     Antibiotic_16 + Antibiotic_17, family = gaussian(), data = ut_data)
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     123.768     42.194   2.933  0.00343 **
## Antibiotic_1S    -6.480     31.618  -0.205  0.83767   
## Antibiotic_2S    12.400     25.817   0.480  0.63112   
## Antibiotic_3S    57.226     25.146   2.276  0.02308 * 
## Antibiotic_4S    28.091     23.063   1.218  0.22351   
## Antibiotic_5S    12.185     21.000   0.580  0.56188   
## Antibiotic_6S    -8.814     20.233  -0.436  0.66322   
## Antibiotic_7S    24.717     19.512   1.267  0.20554   
## Antibiotic_8S    26.984     19.226   1.404  0.16077   
## Antibiotic_9S    12.226     19.011   0.643  0.52031   
## Antibiotic_10S   19.707     18.876   1.044  0.29673   
## Antibiotic_11S   11.280     18.936   0.596  0.55153   
## Antibiotic_12S  -15.182     19.038  -0.797  0.42537   
## Antibiotic_13S    4.128     19.264   0.214  0.83038   
## Antibiotic_14S  -29.553     20.153  -1.466  0.14286   
## Antibiotic_15S  -25.776     20.712  -1.245  0.21360   
## Antibiotic_16S   52.883     22.063   2.397  0.01672 * 
## Antibiotic_17S    4.666     22.683   0.206  0.83708   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 87769.82)
## 
##     Null deviance: 88161184  on 999  degrees of freedom
## Residual deviance: 86189961  on 982  degrees of freedom
## AIC: 14240
## 
## Number of Fisher Scoring iterations: 2

anova(org2_glm, test='LR' )

## Analysis of Deviance Table
## 
## Model: gaussian, link: identity
## 
## Response: Organism_2
## 
## Terms added sequentially (first to last)
## 
## 
##               Df Deviance Resid. Df Resid. Dev Pr(>Chi)  
## NULL                            999   88161184           
## Antibiotic_1   1     3718       998   88157466  0.83693  
## Antibiotic_2   1    35568       997   88121898  0.52439  
## Antibiotic_3   1   410294       996   87711604  0.03061 *
## Antibiotic_4   1   172521       995   87539084  0.16092  
## Antibiotic_5   1    25459       994   87513625  0.59018  
## Antibiotic_6   1     5903       993   87507722  0.79537  
## Antibiotic_7   1   151675       992   87356047  0.18865  
## Antibiotic_8   1   126050       991   87229997  0.23076  
## Antibiotic_9   1    41955       990   87188042  0.48932  
## Antibiotic_10  1   116739       989   87071302  0.24879  
## Antibiotic_11  1    29416       988   87041886  0.56264  
## Antibiotic_12  1    62609       987   86979277  0.39834  
## Antibiotic_13  1    10390       986   86968887  0.73080  
## Antibiotic_14  1   144910       985   86823977  0.19882  
## Antibiotic_15  1   123642       984   86700335  0.23527  
## Antibiotic_16  1   506660       983   86193674  0.01628 *
## Antibiotic_17  1     3713       982   86189961  0.83704  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# compared to:
posterior_interval(org2_stan, prob=0.95)

##                      2.5%     97.5%
## (Intercept)     45.632984 203.66634
## Antibiotic_1S  -66.582505  53.91644
## Antibiotic_2S  -36.551453  62.75136
## Antibiotic_3S    9.291554 107.47275
## Antibiotic_4S  -16.712582  74.14336
## Antibiotic_5S  -30.862366  52.76299
## Antibiotic_6S  -47.668667  28.32247
## Antibiotic_7S  -13.838549  62.30070
## Antibiotic_8S   -9.999097  64.29174
## Antibiotic_9S  -25.943635  50.78890
## Antibiotic_10S -16.271467  55.78870
## Antibiotic_11S -24.797408  47.12190
## Antibiotic_12S -53.942924  23.04457
## Antibiotic_13S -32.265771  41.57003
## Antibiotic_14S -70.609540  10.22694
## Antibiotic_15S -67.230700  13.98810
## Antibiotic_16S   9.934913  96.07911
## Antibiotic_17S -40.190365  49.66852
## sigma          283.425535 309.89830